Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work. (as a seventh grader)
First, we need to find the height of the square pyramid using the Pythagorean theorem.
The slant height (18) is the hypotenuse of a right triangle formed by the height (h) and half the base length (6).
Using the Pythagorean theorem:
h^2 + 6^2 = 18^2
h^2 + 36 = 324
h^2 = 288
h ≈ √288
h ≈ 16.97
Now we can calculate the surface area of the square pyramid using the formula:
Surface Area = base area + (1/2) * perimeter of base * slant height
Base area = 12 * 12 = 144
Perimeter of base = 4 * 12 = 48
Surface Area = 144 + (1/2) * 48 * 18
Surface Area = 144 + 432
Surface Area = 576
Therefore, the surface area of the square pyramid is 576 square units.